Magnetometer and method of detecting a magnetic field

ABSTRACT

The disclosure concerns a magnetometer for detecting a magnetic field, comprising: a solid state electronic spin system containing a plurality of electronic spins and a solid carrier, wherein the electronic spins are configured to be capable of aligning with an external magnetic field in response to an alignment stimulus; and a detector configured to detect an alignment response of the electronic spins, such that the external magnetic field can be detected; wherein the electronic spins are provided as one or more groups, each group containing a plurality of spins, the plurality of spins in each of the one or more groups being arranged in a line that is angled at an angle Θ with respect to the local direction of the external magnetic field at the said group. Also disclosed is a method for detecting a magnetic field.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a U.S. National Stage filing under 35 U.S.C. § 371of International Application No. PCT/GB2019/051641, filed on Jun. 13,2019, which claims the benefit of priority to GB Application No.1809706.3, filed on Jun. 13, 2018.

TECHNICAL FIELD

The present disclosure relates to a magnetometer and to a method ofdetecting a magnetic field.

BACKGROUND

U.S. Pat. No. 8,947,080 (Lukin et al), the contents of which areincorporated herein by reference, describes a magnetometer whichincludes a solid state electronic spin system and a detector. The solidstate electronic spin system contains a plurality of electronic spinsthat are disposed at locations within a solid carrier which in that caseis a single crystal diamond lattice supported by a suitable supportstructure within the magnetometer, for example attached to an opticalwaveguide 610 (see FIG. 6 of U.S. Pat. No. 8,947,080). Furthermore, eachelectronic spin is substantially free of magnetic interference from thecarrier, particularly the remainder of the diamond lattice.

The spins disclosed in U.S. Pat. No. 8,947,080 are nitrogen vacancy (NV)centres within the diamond lattice. An NV centre is a crystallographicdefect in the lattice structure of a single crystal diamond, andconsists of an empty position in the diamond lattice and an adjacentinterstitial atom of an impurity such as nitrogen. NV centres can absorbvisible light and are visible as red spots when illuminated by a laser.The example of an approximately 25 nm diameter diamond nanocrystal withabout 10 NV centres is described in the prior art.

The magnetometer detects an external magnetic field by utilising theeffect that the plurality of electronic spins align with the externalmagnetic field in response to laser optical excitation radiation appliedto the electronic spins.

The magnetic field strength can be quantified by utilising aquantitative effect on the spins that depends on the magnetic fieldstrength. In U.S. Pat. No. 8,947,080, a radiofrequency (RF) field isapplied to the spins aligned in the magnetic field. The RF field inducesthe spins to precess about the magnetic field, the frequency of the spinprecession being linearly related to the magnetic field by the Zeemanshift of the electronic spin energy levels. By detecting output opticalradiation from the electronic spin, the Zeeman shift can be determinedand hence the magnetic field strength.

Desire for magnetometers capable of higher resolution of magnetic fieldmapping and greater sensitivity in the detection of the magnetic fieldpromotes the use of higher densities of spins in the array of electronicspin locations (pixels). However, it has been found that magnetometersensitivity is compromised as the spin density increases. Magnetometersensitivity compromise can result from greater magnetic interferencefrom mutual spin-spin interactions and/or from interactions with thesolid state lattice, leading to a reduced spin coherence time of eachspin. The cause of interactions between the spins may, for example,include dipolar coupling, or exchange coupling at very highconcentrations.

It is further desirable, for miniaturisation and integration of thespins and pixels (sensing elements) containing spins onto electronicchips and other flat substrates, for the spin array to be capable ofbeing made substantially flat (thereby providing a two dimensionalplanar array), rather than the three-dimensional array provided by adiamond crystal lattice.

The present disclosure is based on the surprising finding that at leastsome of the desirable properties discussed above may be obtained byarranging individual spins within an array in a line that is angled at aspecific angle with respect to the local direction of the externalmagnetic field. A preferred value for the specific angle between theline of (S=½) spins and the local external magnetic field is at or nearthe so-called “magic angle” (θ_(m)), which has a value of arccos 1/√3 orarctan √2 (approximately 54.7°). At this preferred angle, the intrinsicinteraction between spins is minimised, and preferably reduced toessentially zero.

Further aspects of embodiments disclose angling the line of (S=½) spinswith respect to the local external magnetic field at other angles,greater or less than the “magic angle”, said other angles being selectedsuch that the intrinsic interaction between spins is substantiallyreduced in comparison with an analogous system in which no specificarrangement of the spins at the angle θ has been performed. Thereduction in the intrinsic interaction may enable a magnetic field to bedetected/measured at the desired sensitivity and spatial resolution.

Further aspects of embodiments disclose the use of higher spins (S>½)with some effective internal alignment axis (for example from a crystalfield) for which the magic angle, at which the intrinsic interactionbetween the spins is minimised, differs from arccos 1/√3.

BRIEF DESCRIPTION OF THE INVENTION

An aspect of an embodiment provides a magnetometer for detecting amagnetic field, comprising: a solid state electronic spin systemcontaining a plurality of electronic spins and a solid carrier, whereinthe electronic spins are configured to be capable of aligning with anexternal magnetic field in response to an alignment stimulus; and adetector configured to detect an alignment response of the electronicspins, such that the external magnetic field can be detected; whereinthe electronic spins are provided as one or more groups, each groupcontaining a plurality of spins, the plurality of spins in each of theone or more groups being arranged in a line that is angled at an angle θwith respect to the local direction of the external magnetic field atthe said group. By arranging the spins in a line that is angled at anangle θ with respect to the local direction of the external magneticfield, the coherence time of the spins is increased relative to anunarranged system, thereby improving the sensitivity of themagnetometer.

The magnetometer may be further configured to perturb the alignment ofthe electronic spins in a manner quantitatively related to the magneticfield strength, and to quantitatively detect the response of theelectronic spins to the perturbation, whereby the magnetic fieldstrength can be measured based on the detected response to theperturbation. In this way, measurements of the magnetic field strengthmay be taken in addition to detecting the presence (and optionallydirection) of the field.

A further aspect of an embodiment provides a method of detecting amagnetic field, comprising: applying an alignment stimulus to a solidstate electronic spin system containing a plurality of electronic spinsand a solid carrier, thereby aligning the electronic spins with themagnetic field; and detecting said alignment response of the electronicspins thereby detecting the magnetic field; wherein the electronic spinsare provided in the solid state electronic spin system as one or moregroups, each group containing a plurality of spins, the plurality ofspins in each of the one or more groups being arranged in a line that isangled at an angle θ with respect to the local direction of the magneticfield at the said group. The method provides improved sensitivityrelative to other method for detecting a magnetic field.

The method may further comprise perturbing the alignment of theelectronic spins in a manner quantitatively related to the magneticfield strength, and quantitatively detecting the response of theelectronic spins to the perturbation, whereby the magnetic fieldstrength can be measured based on the detected response to theperturbation.

Measurement results may be provided on a readout and/or displayapparatus whereby at least one of the presence, direction and strengthof the magnetic field is displayed, preferably at a high spatialresolution across different locations within the magnetic field.Optionally, dynamic display in real time is provided for a variablemagnetic field. Optionally, the display may present the data in two orthree dimensions, or on a screen simulating two or three dimension tothe viewer, corresponding to the desired nature and extent ofmeasurement of the magnetic field.

For example, θ may be between about 45° and about 60°, for examplebetween about 50° and about 57°, for example about 53° and about 56°,for example about 54° and about 55°.

In the most preferred embodiment, θ is the “magic angle” (θ_(m)), whichhas a value of arccos 1/√3 or arctan √2 (approximately 54.7°). At thispreferred angle, the intrinsic interaction between spins in a line isminimised, preferably to essentially zero.

In another embodiment, θ is between about 50° and about 57°. Within thisrange of angles, the intrinsic interaction between spins is reduced toat most about 10% of its nominal value, that is the value that would befound in an with an analogous system in which no specific lining up ofthe spins at the angle θ has been performed, i.e. a random oruncontrolled arrangement.

In another embodiment, θ is between about 45° and about 60°. Within thisrange of angles, the intrinsic interaction between spins is reduced toat most about 25% of its nominal value, that is the value that would befound in an with an analogous system in which no specific lining up ofthe spins at the angle θ has been performed, i.e. a random oruncontrolled arrangement.

The electronic spins are preferably free from magnetic interference fromthe solid carrier. Adjacent groups of electronic spins are preferablyfree from magnetic interference from each other. The expression “freefrom magnetic interference” means that magnetic interference is ruledout or substantially reduced by the nature of the materials involved(typically, this will apply in the case of the solid carrier), and/orthat special measures have been taken, for example by the selection ofthe separation distance between parts, the inclusion of materials thatdampen magnetic interference, or combinations thereof, to rule out orsubstantially reduce the magnetic interference (typically, this willapply in the case of adjacent groups of electronic spins).

The invention allows much higher spin densities to be used thanhitherto, as well as substantially enlarging the range of solid stateelectronic spin systems that can be used in magnetometers. This opensthe possibility of providing highly miniaturised and/or essentiallytwo-dimensional structures for highly sensitive detection of very lowmagnetic field strengths with high spatial resolution, optionally in twoor three dimensions. For example, electronic spin systems with longintrinsic spin coherence times (for example, shallow donor electronspins in silicon), can in principle provide with the present inventionhigh sensitivity magnetometers with the potential for the first time todetect and map magnetic fields with extremely high spatial resolution,for example to about 0.1 nm and even below that, and extremely highsensitivity, for example to about 1 attoTesla and even below that.

DETAILED DESCRIPTION

Solid State Electronic Spin Systems

Any solid state electronic spin system, including surface and bodysystems, known or to be developed, can be used in the implementation ofthe present disclosure.

Examples of suitable spin systems include molecular spin systems, spinsystems based on defects or impurities in inorganic solids, and spinsystems based on the electron spins of artificial atoms such as quantumdots.

Molecular Spin Systems

In molecular spin systems, the spin is typically localised on a metalion surrounded by ligands, or delocalised with a region of an organicmolecule. In both cases, the solvent environment around the moleculeplays a critical role in determining the spin coherence time. Longercoherence times are generally provided by solvents which are essentiallyfree of nuclear spins, such as carbon disulphide (CS₂). In particular, amolecular magnet having ligands that are nuclear-spin-free and aresoluble in CS₂ allowed coherence times of 700 μs to be obtained in a 10Ktesting environment (as discussed in “Millisecond coherence time in atuneable molecular electronic spin qubit” by Zadrozny, J. M. et al., ACSCentr. Sci 1 (9) (2015) 488-492,https://doi.org/10.1021/acscentsci.5b00338 the contents of which areincorporated herein by reference. Web links here and throughout valid asof 5 Mar. 2018.). Molecular spin system can be tethered onto surfaced incarefully defined regions using electron beam lithography patterningcombined with organic linker molecules (see S. K. H. Lam et al., 2008Nanotechnology 19 285303. https://doi.org/10.1088/0957-4484/19/28/285303the contents of which are incorporated herein by reference.).

Spin Systems Based on Defects or Impurities in Inorganic Solids

In these spin systems the solid carrier is an inorganic solid,preferably isotopically pure (having lower than natural abundances ofundesired isotope(s), for example: carbon containing less than 1.1% of¹³C, or silicon containing less than 5% of ²⁹Si). The spin systemsshould preferably contain fewer than about 50 ppm of undesiredisotopes). Defects or impurities are artificially added to the carrierto generate the spin system. The spins are typically located, andpreferably locked in position, in or on the solid carrier.

Spin systems can be based on various solid carriers; suitable substratesinclude silicon, carbon, silicon carbide or zinc oxide. The carbon maybe present in an essentially 2-dimensional system of carbon such asgraphene. The silicon, carbon or silicon carbide is preferablyisotopically enriched such that the ²⁸Si and/or ¹²C isotopespredominate, with all other isotopes present in amounts less thannatural abundance levels. Zinc oxide is isotopically enriched to reducethe ⁶⁷Zn fraction well below natural abundance levels (4%). Theperformance of the systems can be optimised by minimising levels ofundesired isotopes.

Defect sites which provide electronic spin systems can be provided insilicon by doping with donors, for example Group V elements such as P,As, Sb or Bi, or Group VI elements which are singly ionised such as SetDoping using As donors is discussed in greater detail in Spin relaxationand donor-acceptor recombination of Se+ in 28-silicon, R. Lo Nardo etal., Phys Rev B 92 165201 (2015), and doping using Se⁺ donors isdiscussed in greater detail in Stark shift and field ionization ofarsenic donors in 28Si-silicon-on-insulator structures, C. C. Lo et al.,App Phys Lett 104 193602 (2014), the contents of both documents beingincorporated herein by reference.

The silicon used in defect/impurity based spin systems is preferablypredominantly ²⁸Si formed by isotopic enrichment, with a remaining ²⁹Siconcentration down to 50 ppm. Using Group V donors and cooling belowabout 50K, electrons become bound to the donor atom, with an isotropichyperfine coupling to the donor nucleus. The electron spins of suchdonors have coherence times which are limited to several hundreds ofmicroseconds in natural abundance silicon (5% ²⁹Si), but can reach tensof milliseconds in ²⁸Si with [P]=10¹⁴ cm⁻³, limited only byinstantaneous diffusion caused by the finite concentration of donorelectron spins (see, for example, Tyryshkin et al, “Coherence of spinqubits in silicon”, J. Phys.: Condens. Matter, 18 (21), (2006), S783(URL: http://stacks.iop.org/0953-8984/18/i=21/a=S06); George et al,“Electron spin coherence and electron nuclear double resonance of Bidonors in natural Si”, Phys. Rev. Lett. 105 (2010) 067601 (URL:https://doi.org/10.1103/PhysRevLett.105.067601); and Tyryshikin et al,“Electron spin coherence exceeding seconds in high-purity silicon”, Nat.Mater. 11(2) (2011), 143-147 (URL:http://www.ncbi.nlm.nih.gov/pubmed/22138791), the contents of all ofwhich are incorporated herein by reference.

Defect sites which provide electronic spin systems can be provided incarbon using NV centres in single diamond nanocrystals, such asdescribed in U.S. Pat. No. 8,947,080 (Lukin et al) and US PatentApplication No. 2010/0315079 (Lukin et al, see also Jelezko et al,“Observation of coherent oscillations in a single electron spin”, Phys.Rev. Lett., 92(7) (2004), 1-4 (URL:http://link.aps.org/doi/10.1103/PhysRevLett.92.076401)). The large Debyetemperature of diamond, coupled with the mainly nuclear-spin-free carbonenvironment, leads to electron spin coherence times of several hundredmicroseconds at room temperature, extendible to a few milliseconds usingdecoupling via the CPMG (Carre-Purcell-Meiboom-Gill) periodic pulsesequence (see Bar-Gill et al, “Solid-state electronic spin coherencetime approaching one second”, Nat. Commun. 4 (2013), 1743 (URL:http://www.ncbi.nlm.nih.gov/pubmed/23612284) or by using ¹²C-enricheddiamond (Balasubramanian et al, “Ultralong spin coherence time inisotopically engineered diamond”, Nat. Mater. 8 (2009), 383-387).Alternatively, silicon vacancy (SiV⁻¹) (S=½; T₂ approximately 100 ns at3.6 K) or germanium vacancy (GeV⁻¹) (T*₂ approximately 20 ns at 2.2 K)defects can be introduced into single diamond nanocrystals to providespin systems The use of the negatively charged silicon vacancy defectsin carbon is described in Pingault et al, “Coherent control of thesilicon-vacancy spin in diamond”, Nat. Commun. 8 (2017), 15579 andRogers et al, “All-optical initialization, readout, and coherentpreparation of single silicon-vacancy spins in diamond”, Phys. Rev.Lett. 113 (2014), 263602 (URL:https://link.aps.org/doi/10.1103/PhysRevLett.113.263602). The use of thenegatively charged germanium vacancy defects in carbon is described inSiyushev et al, “optical and microwave control of germanium-vacancycentre spins in diamond”, Phys. Rev. B 96, 081201 (2017)(https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.081201) andBhaskar et al, “Quantum nonlinear optics with a germanium-vacancy colorcentre in a nanoscale diamond waveguide”, Phys. Rev. Lett. 118 (2017),223603 (URL: https://link.aps.org/doi/10.1103/PhysRevLett.118.223603).The neutral SiV⁰ centre (S=1, in contrast, has T₂ approximately 1 ms at20 K, while still retaining most (90%) of its optical emission in thezero phonon line, a combination which makes it very promising (see Rose,et al, “Observation of an environmentally insensitive solid state spindefect in diamond” (https://arxiv.org/abs/1706.01555). For sensing,nanodiamonds are also used but they have much shorter coherence times asshown by Knowles et al, “Observing bulk diamond spin coherence inhigh-purity nanodiamonds”, Nat. Mat. 13, 2 21-25 (2014)(https://www.nature.com/articles/nmat3805). Spins near the surface ofthe diamond can be closer to the magnetic field to sense, but they areharder to fabricate and have coherence time strongly affected by thesurface, as studied by de Oliveira et al, “Tailoring spin defects indiamond by lattice charging”, Nat. Comm. 8, 15409 (2017)(https://www.nature.com/artides/ncomms15409). The contents of all thereferences identified above in this paragraph are incorporated herein byreference.

Defect sites which provide electronic spin systems can be provided insilicon carbide, another host offering a largely nuclear-spin-freeenvironment (see Seo et al, “Quantum decoherence dynamics of divacancyspins in silicon carbide”, Nat. Commun. 7 (2016) 12935(https://www.nature.com/ncomms/2016/160929/ncomms12935/full/ncomms12935.html)Suitable defects include neutral divacancies in 4H-SiC, for exampleneutral divacancies established by irradiation with 2 MeV electrons at arange of fluences from about 5×10¹² cm⁻² to about 1×10¹⁵ cm⁻² to createSi and C vacancies, followed by annealing to activate vacancy migration.See, for example, Christle et al “Isolated electron spins in siliconcarbide with millisecond coherence times (available on-line athttps://arxiv.org/ftp/arxiv/papers/1406/1406.7325.pdf); Falk et al,“Polytype control of spin qubits in silicon carbide”, Nat. Commun. 4,1819 (2013); and Carlos et al, “Annealing of multivacancy defects in4H-SiC”, Phys. Rev. B 74, 235201 (2006), the contents of all of whichare incorporated herein by reference.

Defect sites can also be provided by rare earth dopants in crystalhosts, such as yttrium orthosilicate (YSO) and YLiF₄. Spin coherencetimes of in excess of one second have been observed in erbium (Er) dopedYSO when subjected to both high magnetic fields (such as 7T) and lowtemperatures (1.4K), said conditions being required to suppress electronspin dynamics.

Electron spins can also be confined in quantum dot structures, forexample in metal-oxide-semiconductor (MOS) structures and Si/SiGeheterostructures. The coherence lifetimes of such systems can reach 28ms under dynamical decoupling (as discussed in “An addressable quantumdot qubit with fault-tolerant control-fidelity”, M. Veldhorst et al.,Nature Nanotechnology 9, 981-985 (2014), doi:10.1038/nnano.2014.216incorporated herein by reference) and using ²⁸Si. Though not as long acoherence time as the longest times of atomic defect spins in solids,quantum dots have the advantages of highly controlled placement accuracythrough fabrication methods and well developed read-out schemes, asdiscussed below.

The electron spin systems may be used at cryogenic temperatures, forexample less than about 100 K, in order to provide preferable spincoherence time. The temperatures required to provide suitable coherencetimes in a given system are dependent primarily upon the solid carrierused in the system. For example, Si based systems are typically operatedat temperatures less than about 10K, while systems based on C or SiC ormolecular electron spins can have effective operational temperaturesranging from less than about 1K to room temperature. Quantum dot spinsare typically measured at temperatures below 1K. As such, theoperational temperature is set based on the particular coherencerequirements of each system.

Alignment/Polarisation

Any suitable spin alignment stimulus can be applied a solid stateelectronic spin system in accordance with the present disclosure. Anexample of a suitable alignment stimulus utilises an applied externalmagnetic field. In the example alignment mechanism, the spins are firstpolarised using an applied external magnetic field. The externalmagnetic field may be generated by driving a set current through coilsin a Helmholtz arrangement, or using a permanent magnet (such as Fe orCo or rare-earth-based compound) in the vicinity of the sample, or usingthe Earth's magnetic field.

Alternatively or additionally, some systems may be polarised usingincident electromagnetic radiation. That is, some systems can beoptically polarised by applying optical illumination incident of thespins at a precise wavelength (and therefore energy) suitable forabsorption by the spin. In some instances, the spin is polarizedoptically via a spin-dependent intersystem crossing. For negativelycharged nitrogen vacancy (NV) centres in diamond, the illuminationwavelength used for spin polarisation may be in the visible region, forexample using a wavelength of 532 nm. In negatively charged siliconvacancies, the excitation wavelength may be at higher wavelength, forexample between 700 nm and 920 nm (Baranov, P. G. et al. Silicon vacancyin SiC as a promising quantum system for single-defect and single-photonspectroscopy. Phys. Rev. B 83, 125203 (2011)). In neutral divacancies insilicon carbide, the wavelength may be in the near-infrared, for examplebetween 800 and 1150 nm (Koehl, W. F., et. al. Room temperature coherentcontrol of defect spin qubits in silicon carbide. Nature 479, 84-87(2011)). Donor spins in silicon may be optically polarised usingdonor-bound exciton transitions around 1078-1080 nm (Lo et al, NatureMaterials 14 490 (2015)). The contents of all the references identifiedabove in this paragraph are incorporated herein by reference

Spin Alignment Detection Devices and Field Detection

In order to obtain the magnetic field, the alignment of the spins isdetected using a suitable alignment detection device. From the detectedspin alignment the presence (and direction) of the magnetic field isdeduced.

To detect their state, the spins may be manipulated using a microwave orradiofrequency pulse of precise frequency, phase and duration in orderto convert the states which have evolved as a result of a magnetic fieldto which the spins are subjected into states which are readilydistinguishable by measurement.

For optically-active defects in the solid state, such as nitrogenvacancy centres in diamond, silicon vacancy centres in diamond, siliconvacancies in silicon carbide or divacancies in silicon carbide, the spinalignment may be measured for example via spin-dependentphotoluminescence. In this process, the photoluminescence afterexcitation by a laser source depends on the alignment of the spin in theground or excited state due to an inter-system crossing. The methods forpolarization (as discussed above) and measurement are very similar inthis case, in particular the methods typically include the applicationof electromagnetic radiation of the same wavelength. For nitrogenvacancy centres in diamond, the illumination wavelength may be forexample 532 nm and the centres emit light from about 600 to 800 nm. Fordivacancies in silicon carbide, the illumination wavelength may be forexample 975 nm and the centres emit light from about 1050 to 1200 nm.

Donor electron spins in silicon and quantum dot spins can be readthrough a process of spin-to-charge conversion. This can be achieved byspin-dependent donor or dot ionisation through tunnelling of the donoror dot electron to an electron reservoir in a silicon nanodevice, causedby the difference in the spin-up and spin-down energy levels in amagnetic field (Elzerman et al, Nature 430, pages 431-435 (22 Jul.2004)). The change in the donor or dot charge state is detected by asingle electron transistor, to yield the state of the donor or dot spin(spin-up or spin-down, i.e. aligned with or against the externalmagnetic field) (Pla et al. Nature 489 541-545 (2012)). Spin-dependentdonor or dot isolation typically requires very low temperatures andlarge magnetic fields to work effectively (e.g. 3 Tesla and 100 mK).

An alternative strategy for spin-to-charge conversion for donors insilicon, which is less temperature and magnetic field dependent and canwork down to zero magnetic field and temperatures of up to 10K, is basedon the spin-selective generation of donor-bound excitons, a methoddemonstrated for example in Lo et al, Nature Materials 14 490 (2015).Here the donor-bound exciton is optically generated using a laser pulse,in a manner which depends on the spin-state of the donor. Thedonor-bound exciton then decays by Auger recombination, ionising thedonor. The resulting donor ionisation can be detected using methodsincorporating a single electron transistor, or by RF gate reflectometry,or by the generated photocurrent or some other change in the compleximpedance of the device, as would be understood by those skilled in theart. The contents of all the references identified above in thisparagraph are incorporated herein by reference

Spin Alignment Perturbation Devices and Field Strength Measurement

In order to quantify the external magnetic field a perturbation, theeffect of which is quantitatively related to the magnetic fieldstrength, may be applied to the aligned spins.

After alignment/polarisation, the spins may be given some form offurther stimulus, for example using a microwave or radiofrequency pulseof precise frequency, phase and duration, to excite them into aparticular quantum state which will evolve, for example picking upphase, as a result of the magnetic field to be sensed. Afteralignment/polarisation, the spins may also be continuously driven by,for example, a microwave or radiofrequency excitation in order tomeasure the resonance frequency of the spins. This resonance frequencymay be sensitive to the external magnetic field to be sensed. Thesensing is realized by detecting changes in the resonance frequency.

In one embodiment, the spins are rotated by the ESR (electron spinresonance) field or radio frequency (RF) radiation into the x-y plane(i.e. a plane perpendicular to the initial spin alignment direction),and then the external magnetic field to be measured causes the spins toprecess about the direction of the magnetic field.

The spins may be manipulated further during the sensing period in orderto make them sensitive only to time-varying (AC) magnetic fields ofparticular frequency.

The perturbation of aligned spins in aspects of embodiments may beperformed using any of the methods discussed above. In particular, thesemethods are suitable for use with: molecular spin systems; spin systemsof silicon provided with Group V donors providing an electronic spin;spin systems of carbon provided with NV centres, negative siliconvacancies, neutral silicon vacancies or germanium vacancies; and spinsystems of silicon carbide provided with neutral divacancies providingan electronic spin.

Embodiments of the Arrangements of Electronic Spins into Groups and theAngulation Thereof

Localised spins are formed in arrays with specific geometries, which canbe created using established micro-fabrication processes. Typically thesensitivity of spin based magnetometers depends on the number of spinsin each pixel, or sensing element, with the sensitivity beingapproximately proportional to the square root of the number of spins (N)(therefore ˜N^(1/2)). The sensitivity is also approximately proportionalto the square root of the spin coherence time of each spin (˜√{squareroot over (T₂)}). Typically increasing the number of spins (N) resultsin a reduced T₂, due to the increased magnetic dipolar interactionbetween the spins.

In aspects of embodiments of the present disclosure, the spins areprovided as one or more groups each containing a plurality of spins, thespins of a group being present in a substantially straight line which isangled at an angle θ with respect to the local direction of the magneticfield at the group.

The spins may be arranged in a single line, also referred to as a stripeor a chain. However, in aspects of embodiments of the disclosure, thenumber of spins may be further increased by providing a plurality oflines (also referred to as stripes or chains) of spins. A magnetometermay comprise multiple pixels or sensing elements, each of whichcomprises one or more lines (stripes, chains) of spins. These stripesmay, for example, be arranged substantially parallel to each other ineach pixel and/or in the overall pixel array of the magnetometer. Thelateral spacing between each stripe (also referred to as the inter-chainseparation) is preferably selected to be sufficiently large such thatthe interactions between dipoles in adjacent stripes is negligiblysmall. The lateral spacing between stripes, and also the intra-chainspacing between spins, is dependent upon the specific configuration ofthe system, for example, the nature of the spins, a type of solidcarrier or solvent that is used, and so on. Typical lateral spacings areof the order of 750 nm. By way of example, intra-chain spacings betweenspins can typically be of the order of 10 to 100 nm.

Data Output and Display Devices

In accordance with the present disclosure, an array of spins may befabricated to form the pixels of a magnetometer, for example as asilicon based semiconductor device in the manner of known CCD (ChargeCoupled Device) or active pixel sensor (APS) arrays. The localised spinstates are detected by a hybrid optical-electrical detection method,where photons at a particular wavelength are used to excite thelocalised spin states, creating free charges that can be captured. Theresulting transient current/charge accumulation is detected byintegrated on-chip electronics.

The magnetometer may include apparatus for recording and/or displayingthe data output. Electrical and electronic means may be provided suchthat the raw data output may be saved for later processing, or may beprocessed immediately, to determine properties of the magnetic field.Properties of the field to be determined may include, for example, thefield presence, field strength and/or field direction. The data may berecorded at a high spatial resolution and may be an instantaneousmeasurement, or recorded over a period of time, or a series ofindividual measurements may be taken over a period of time to providedetails of how the field changes with time. Such data may be savedwithin the apparatus or on any suitable recording medium, for example ahard disk drive, random access memory (RAM), optical disk or disks, andso on. The data may be saved locally and/or may be transmitted over asuitable network, such as the internet, for remote storage orprocessing.

Alternatively, or in addition to the above, the magnetometer may presentmeasurements to a user in real time, or in near real time (for example,real time plus a constant delay).

The magnetometer may comprise a display device. A dynamic display inreal time may be provided for a variable magnetic field. The display maypresent the data in two or three dimensions, or on a screen simulatingtwo or three dimension to the viewer, corresponding to the desirednature and extent of measurement of the magnetic field.

Sensitivity and Spatial Resolution

A magnetometer as described herein may provide a sensitivity of around 1pT/Hz^(−1/2) for a pixel area of 30×30 μm². The sensitivity provided byany given magnetometer in accordance with the present disclosure isdetermined primarily by the square root of the area of the sensor, suchthat a pixel area of 100×100 μm² may provide a sensitivity of around 300fT/Hz^(−1/2).

In some aspects of embodiments the sensing area of the magnetometer maybe as small as 10×10 μm². By way of comparison, a known SQUID(Superconducting QUantum Interference Device) sensor with a 30×30 μm²area has a sensitivity of around 2 pT/Hz^(−1/2). However the sensitivityof a SQUID sensor scales linearly with area. Therefore, aspects ofembodiments of the present invention provide magnetometers that mayperform substantially better than SQUID sensors of equivalent sensingareas, especially but not exclusively for small sensor areas such as,for example areas smaller than 30×30 μm².

Manufacture/Fabrication of the Magnetometer and Spin Systems

Donor spins may be created in semiconductors, such as silicon, usingmethods such as scanning tunnelling microscopy (STM) based lithography,as known to those skilled in the art. Use of suitable manufacturingmethods can provide atomic precision accuracy in the placement ofindividual spins. Suitable methods are known to those skilled in theart.

The creation of the spin arrays requires confinement of the dopingprofile in two dimensions. This may be achieved for example usingone-dimensional materials such as nanowires or nanopillars (Babinec, T.M. et. al. A diamond nanowire single-photon source, NatureNanotechnology 5, 195-199 (2010)). This may also be achieved bycombination of two separate techniques for each dimension ofconfinement. Depth confinement may be created for example bydelta-doping techniques where a single layer of material with dopants ordefects is created (Ohno, K. et. al. Engineering shallow spins indiamond with nitrogen delta-doping. Appl. Phys. Lett. 101, 082413(2012)). Lateral confinement may be realized for example usingnanofabrication technique such as etching or implantation through apatterned mask, written by electron-beam or optical lithography. Lateralconfinement may also be generated by selective ionization using metallicgates or other methods. The present invention may be insensitive tosmall misalignment of spins in the arrays. The misalignment must be afraction of the inter-spin spacing within an array which may be definedby the spin concentration. Quantum dot spins for example MOS or Si/SiGeare confined using patterned metal gates and hence linear arrays can beproduced simply by repeating the structure which forms the quantum dotalong one dimension. Using typical gate pitches and current fabricationtechnology, intra-chain spacings of 20-30 nm are possible, and smallerspacings can be expected from further development of advancedfabrication methods. The contents of all the references identified abovein this paragraph are incorporated herein by reference

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments of the present invention are now described, by wayof example only, with reference to the accompanying Figures in which:

FIG. 1A is an example of the magnetic field due to a magnetic dipole;

FIG. 1B is an example of a magnetic dipole showing the “magic angle”;

FIGS. 2A-2B are examples of electronic spin systems, FIG. 2A notaccording to the present invention and FIG. 2B according to the presentinvention;

FIGS. 3A-3B are examples of a pixel of a magnetometer;

FIGS. 4A-4B show simulations of spin coherence time for themagnetometers in FIGS. 3A-3B;

FIG. 5 is a schematic diagram showing a magnetometer system inaccordance with an aspect of an embodiment; and

FIG. 6 is a flow diagram showing an example of a method of detecting amagnetic field.

DETAILED DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a magnetic dipole 102, and the corresponding magneticfield lines 104. With the dipole aligned in the ‘z’ direction, the fieldstrength is given by the equation:{right arrow over (B)}=|μ|/r ³(3 sin θ cos θ(cos ϕ{circumflex over(x)}+sin ϕŷ)+(3 cos ²θ−1){circumflex over (z)})where μ is the magnetic dipole moment, (r, θ, ϕ) are polar coordinates.

FIG. 1B also shows a magnetic dipole 102 orientated in the ‘z’direction, and shows regions in which the ‘z’ component of the magneticfield, B_(z), are positive 104 and regions in which B_(z) is negative106. There exists a line 110 between these regions, along which B_(z) iszero. The angle formed between this line and the direction oforientation of the dipole 102 is known as the “magic angle”, and it hasa value of θ=arccos 1/√{square root over (3)}≈54.7° as describedpreviously.

FIG. 2A shows a known solid state electronic spin system 200 comprisinga plurality of electronic spins 202 a, 202 b, 202 c generally alignedwith a magnetic field 204. The electronic spins are positioned randomlywithin a solid carrier. Due to the random angles between the positionsof the magnetic dipoles of the spins 202 a, 202 b, 202 c, there exists amagnetic dipolar interaction between the electronic spins 202 a, 202 b,202 c. This dipolar interaction reduces the spin coherence time T₂ ofeach spin 202 a, 202 b, 202 c.

FIG. 2B shows a solid state electronic spin system 210, according to thepresent disclosure, comprising a plurality of electron spins 212 a, 212b, 212 c generally aligned with a magnetic field 214. In this system 210the electronic spins 212 a, 212 b, 212 c are not randomly arranged as inFIG. 2A, but instead are arranged along a substantially straight line216. Typically a line will include a plurality of spins, generally 3 ormore spins, and may contain at least one hundred, several hundred orseveral thousand spins.

The line 216 forms an angle θ (218) with the magnetic field 214, thevalue of the angle θ being approximately equal to the ‘magic angle’described in relation to FIG. 1 . It has been established that at thismagic angle there is little or no unwanted dipolar interaction betweenthe spins 212 a, 212 b, 212 c and so the spins in the electronic spinsystem 210 shown in FIG. 2B have a surprisingly long spin coherence timerelative to the spin coherence time of a randomly or uncontrolledlyarranged electronic spin system 200, such as the system shown in FIG.2A. It is not essential for the line of spins to be provided at exactlythe magic angle with respect to the magnetic field 214; a larger rangeof angles may be used without negating the increase in coherence timeprovided by the arrangement of the spins. Although the exact range ofangles which may be used without negating the increased coherence timebenefits is dependent on the specific system configuration, typicalrange of angles which provide substantial increases in coherence timesrelative to unarranged spin systems are between about 45° and about 60°.Preferably, the angle is between about 50° and about 57°, morepreferably between about 53° and about 56°, even more preferably betweenabout 54° and about 55°. The closer the angle is to the magic angle(54.7°), the more pronounced the coherence time benefits provided are.As stated above, for spins with S>½ under the influence of some crystalfield, the optimum angle differs from 54.7° and should be setaccordingly.

FIG. 3A shows a pixel of a magnetometer 300 in accordance with an aspectof an embodiment. The magnetometer pixel 300 comprises a solid carrier302. The solid carrier may be formed from, for example, a semiconductingmaterial such as silicon. Within the solid carrier 302 there are aplurality of electronic spins 304. The plurality of electronic spins 304are arranged using any suitable method in a line as described inrelation to FIG. 2B. The orientation of the line of spins 304 is suchthat it forms an angle 306 with the magnetic field to be measured 308.As described previously, the angle 306 is be selected so that it is theangle θ in accordance with the present invention, namely at or near the“magic angle”.

FIG. 3B shows a pixel of a magnetometer 310 in accordance with a furtheraspect of an embodiment. The magnetometer pixel 310 also comprises asolid carrier 312 and a plurality of electronic spins 314. However theelectronic spins are arranged in several lines 314 a, 314 b, 314 c, 314d rather than in a single line. This allows more electronic spins to beprovided within the magnetometer pixel. The spacing 316 between thelines of electronic spins is selected that it is sufficiently large thatthere is no significant interaction between the spins in adjacent lines,that is, any interaction between spins in adjacent lines does not negatethe increase in spin coherence time of the system provided by aligningthe electron spins in lines. An example of a suitable spacing betweenlines is 750 nm, although this value is dependent upon the specificconfiguration of the system.

The spacing 318 between of the spins within a given line may, however,be substantially smaller than the lateral spacing 316 between lines,without negatively impacting upon the spin coherence time. Typicalexamples of intra-line spin spacings are between 10 and 100 nm, althoughagain the exact value is dependent upon the specific systemconfiguration. The relatively close proximity of the spins within a lineis acceptable because the spins within the line do not mutuallyinterfere to an extent sufficiently large to overcome positive effectson the spin coherence time; preferably the spins within a line arearranged at or near the angle θ with respect to the local direction 308of the magnetic field.

FIGS. 4A and 4B show the simulated Electron Spin Echo (ESE) for themagnetometers shown in FIGS. 3A and 3B, respectively. The vertical axisof the figures represents the angle θ between the line of electronicspins and the applied external magnetic field. The horizontal axisrepresents spin coherence time τ. FIG. 4A shows the ESE intensity forthe magnetometer with a single line of electronic spins, and shows apeak in the ESE intensity around the angle of 54.7°. As discussed above,54.7° is the angle at which a reduced interaction between electronicspins is observed; the “magic angle”.

FIG. 4B shows a similar plot to that shown in FIG. 4A, save that themagnetometer to which the ESE shown in FIG. 4B relates comprises aplurality of parallel lines of electronic spins (as shown in FIG. 3B). Apeak in ESE intensity can also be seen around the “magic angle”, howeverthis peak is less intense than that of FIG. 4A, due to the magneticdipole interactions between spins in adjacent lines. Despite themagnetic dipole interactions between spins in adjacent lines, the spincoherence time of the magnetometer is substantially longer than would bethe case for a magnetometer having randomly arranged electron spins.

FIG. 5 is a schematic diagram showing a magnetometer system inaccordance with an aspect of an embodiment. For simplicity, themagnetometer shown in FIG. 5 shows a single pixel comprising an array ofspins 504; typically a magnetometer would comprise a plurality of suchpixels. The spin array 504 of FIG. 5 comprises a plurality of spins 504a supported by a substrate 504 b solid carrier. Typically, the spins 504a are locked in position with respect to one another in or on the solidcarrier, and the magnetometer comprises means for moving the pluralityof spins 504 a collectively with respect to the local magnetic field.Alternatively, and depending on the specific configuration and purposeof the magnetometer, a local magnetic field source may be moved withrespect to the plurality of spins 504 a. In a further aspect of anembodiment, wherein the spins are confined in quantum dot structures,the respective positions of the spins relative to one another (and alocal magnetic field) may be varied by manipulating gate potentials. Inthis further aspect, the relative spin positions may be manipulatedusing gate potential variations.

The orientation axis of the spins may be determined by an externallyapplied magnetic field “bias field” 510 or other properties of the spin,such as in internal crystal field. Where optical hyperpolarisation isused, this is provided from an optical source 506 such as a laser. Thespins are subjected to an alignment stimulus such as an electromagneticwave pulse from an RF source 502 (typically a microwave or radiofrequency pulse, although pulses from other regions of theelectromagnetic spectrum may also be used, as can continuous waveexcitation) of precise frequency, phase and duration in order to convertthe states which have evolved as a result of an additional magneticfield (on top of the bias field) to which the spins are subjected intostates which are readily distinguishable by measurement. The propertiesof the electromagnetic wave pulse used (that is, the frequency, phase,duration, etc.) are selected according to the nature of the spin array504. Following the application of the alignment stimulus by the sourceand detector 506, the alignment response of the spins is detected by thedetector 506, which may include electrical and/or optical sourceelements. As such, both the presence and direction (or just thepresence) of a magnetic field may be detected. The spins mayphotoluminesce following excitation by the optical source in 506, inwhich case optical detector in 506 may use photomultiplier tubes,photodiodes or similar to detect the emitted photons. Additionally oralternatively, the spins may be ionised (for example, using opticalfrequency light). A subsequent change in charge state or electronemission due to the ionisation may then be detected using an electricaldetector 506. The response of the spin array 504 to the perturbationstimulus from the RF source 502 can be used to quantify the propertiesof the spin array in greater detail. In particular, the strength of themagnetic field may be determined based on an analysis of the response tothe perturbation stimulus.

The source and detector 506 is connected to a controller and interface508. This is responsible for triggering the initial alignment stimulus,and receiving the detector readout from the source and detector 506. Thecontroller and interface 508 is typically linked to further components(not shown), such as a display unit or readout for indicating theresults of the measurement, and/or a memory unit that may be used tostore the results for future analysis. Optionally, the controller andinterface 508 may be connected to a network (such as a LAN or theInternet) such that the results of the measurement may be distributedfor interpretation at a local or remote site.

Similarly to the source and detector 506, the RF source 502 is connectedto a controller and interface 508. Where a pulsed source 502 is used,the controller and interface 508 is responsible for triggering the pulseemission. Where a CW source 502 is used, this triggering is notnecessary. The response of the spin array 504 to the perturbationstimulus is detected by the source and detector 506, and the detectionresults are then passed to the controller and interface 508. As in thecase of the initial alignment stimulus results, a display unit may beused for indicating the results of the measurement, and/or a memory unitmay be used to store the results for future analysis. Where thecontroller and interface 508 is connected to a network (such as a LAN orthe Internet), this may be used to distribute results for interpretationat a local or remote site. The calculation of the magnetic fieldproperties (such as presence, optionally direction, optionally strength,and so on) may be calculated at the controller and interface, oralternatively the raw results may be transmitted as discussed above suchthat the magnetic field properties can be calculated elsewhere.

FIG. 6 shows a flowchart of a method of detecting a magnetic fieldaccording to an aspect of an embodiment. The method may be executedusing a suitable magnetometer, such as the magnetometer shownschematically in FIG. 5 . As illustrated in block 602, the methodcomprises applying an alignment stimulus to a solid state electronicspin system containing a plurality of electronic spins and a solidcarrier. The application of the alignment stimulus (as discussed)results in the alignment of the electronic spins with the magneticfield. The electronic spins are provided in the solid state electronicspin system as one or more groups each containing a plurality of spins,the spins of a group being present in a line which is angled at an angleθ with respect to the local direction of the magnetic field at the saidgroup. As discussed above, θ is an angle at which the intrinsicinteraction between the spins is sufficiently reduced, in comparisonwith an analogous system in which no specific or deliberate arrangementof the spins at the angle θ has been performed. The method allows themagnetic field to be detected, and optionally its strength measured, ata desired sensitivity and spatial resolution.

In block 604 the method optionally comprises perturbing the alignment ofthe electronic spins in a manner quantitatively related to magneticfield strength. In block 606 the method comprises detecting saidalignment response of the electronic spins and optionally saidperturbation of the said alignment, thereby detecting the magnetic fieldand optionally quantifying its strength.

The foregoing broadly describes the present disclosure withoutlimitation. Variations and modifications as would be readily apparent tothose skilled in the art are intended to be included. For the avoidanceof doubt, the scope of the invention is defined by the claims.

The invention claimed is:
 1. A magnetometer for detecting a magneticfield, comprising: a solid state electronic spin system containing aplurality of electronic spins and a solid carrier, wherein theelectronic spins are configured to be capable of aligning with anexternal magnetic field in response to an alignment stimulus; and adetector configured to detect an alignment response of the electronicspins, such that the external magnetic field can be detected; whereinthe electronic spins are provided as one or more groups, each groupcontaining a plurality of spins, the plurality of spins in each of theone or more groups being arranged in a line that is angled at an angle θwith respect to the local direction of the external magnetic field atthe said group, wherein the angle θ is between about 45° and about 60°.2. A magnetometer according to claim 1, further configured to perturbthe alignment of the electronic spins in a manner quantitatively relatedto the magnetic field strength, and to quantitatively detect theresponse of the electronic spins to the perturbation, whereby themagnetic field strength can be measured based on the detected responseto the perturbation.
 3. A magnetometer according to claim 1, furtherincluding a readout and/or display apparatus configured to indicate atleast one of the presence, direction and strength of the magnetic fieldat a plurality of locations within the magnetic field.
 4. A magnetometeraccording to claim 1, wherein each spin of a given group of spins ispositionally locked in mutual alignment in or on the solid carrier withrespect to other spin(s) in the group, wherein the magnetometer mayoptionally further comprise means for moving the group of spinscollectively and/or moving the local magnetic field in order to achievethe desired angular alignment of the group of spins with the magneticfield.
 5. A magnetometer according claim 1, wherein each spin of a givengroup of spins is positionally adjustable with respect to the otherspin(s) of the group of spins, wherein the magnetometer may optionallyfurther comprise means for moving all the spins of the group and/or thelocal magnetic field, for adjustment of the alignment according to thelocal direction of the magnetic field.
 6. A magnetometer according toclaim 1, wherein θ is between about 50° and about 57°, preferablywherein θ is between about 53° and about 56°, more preferably wherein θis between about 54° and about 55°.
 7. A magnetometer according to claim6, wherein θ is 54.7°.
 8. A magnetometer according to claim 6, which hasa sensitivity to about 1 attoTesla and a spatial resolution to about 0.1nm.
 9. A magnetometer according to claim 1, wherein the electronic spinsystem consists of or includes at least one of: molecular spin systems;spin systems of silicon provided with Group V donors providing anelectronic spin; spin systems of carbon provided with NV centres,negative silicon vacancies, neutral silicon vacancies or germaniumvacancies; and spin systems of silicon carbide provided with neutraldivacancies providing an electronic spin.
 10. A magnetometer accordingto claim 1, wherein each group comprises at least 3 electronic spinsarranged in a line, preferably wherein each group comprises at least 100electronic spins arranged in a line.
 11. A method of detecting amagnetic field, comprising: applying an alignment stimulus to a solidstate electronic spin system containing a plurality of electronic spinsand a solid carrier, thereby aligning the electronic spins with themagnetic field; and detecting said alignment response of the electronicspins thereby detecting the magnetic field; wherein the electronic spinsare provided in the solid state electronic spin system as one or moregroups, each group containing a plurality of spins, the plurality ofspins in each of the one or more groups being arranged in a line that isangled at an angle θ with respect to the local direction of the magneticfield at the said group, wherein the angle θ is between about 45° andabout 60°.
 12. A method according to claim 11, further comprisingperturbing the alignment of the electronic spins in a mannerquantitatively related to the magnetic field strength, andquantitatively detecting the response of the electronic spins to theperturbation, whereby the magnetic field strength can be measured basedon the detected response to the perturbation.
 13. A method according toclaim 11, wherein θ is between about 50° and about 57°, preferablywherein θ is between about 53° and about 56°, more preferably wherein θis between about 54° and about 55°.
 14. A method according to claim 13,wherein θ is 54.7°.
 15. A method according to claim 13 which has asensitivity to about 1 attoTesla and a spatial resolution to about 0.1nm.
 16. A method according to claim 11, wherein the electronic spinsystem consists of or includes at least one of: molecular spin systems;spin systems of silicon provided with Group V donors providing anelectronic spin; spin systems of carbon provided with NV centres,negative silicon vacancies, neutral silicon vacancies or germaniumvacancies; and spin systems of silicon carbide provided with neutraldivacancies providing an electronic spin.
 17. A method according toclaim 11, wherein each group comprises at least 3 electronic spinsarranged in a line, preferably wherein each group comprises at least 100electronic spins arranged in a line.